SOLUTION: how to find Find the center, vertices, foci and asymptotes of this equation {{{ 9x^2 - y^2 + 18x + 6y - 4 = 0}}}

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Question 862560: how to find Find the center, vertices, foci and asymptotes of this equation
+9x%5E2+-+y%5E2+%2B+18x+%2B+6y+-+4+=+0
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the Squares for the x and the y and adjust to standard form equation. The form possible will tell you which conic section is the equation.

That alone is not enough; but you should be able to check your textbook instruction as a reference for more information about foci and asymptotes for the particular conic section you found. The center and vertices are the easy parts.

The term for completing the square for the x is 1, as long as first factor the 9 from the terms with x; and the term for completing square for the y is 9, as long as you factor a negative 1 from the terms of y first. You also must use additive inverses to maintain equality.

One of the steps will look like this:
9%28x%5E2%2B2x%2B1%29-%28y%5E2-6y%2B9%29-4-9%2B9=0

Further steps should produce this:
highlight%28%28x%2B1%29%5E2%2F%282%2F3%29%5E2-%28y-3%29%5E2%2F2%5E2=1%29.
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HYPERBOLA, centered at (-1,3), vertices at x=-1-2%2F3 and x=-1%2B2%2F3 both with y=3. The a value in reference to standard form, is a=2%2F3; and the b value is b=2. Each focus is a distance c from the center point, and the relationship among a, b, and c is a%5E2%2Bb%5E2=c%5E2, so you can now find the value of c.